On the entropy devil's staircase in a family of gap-tent maps

Details On the entropy devil's staircase in a family of gap-tent maps On the entropy devil's staircase in a family of gap-tent maps

1998-07-07

arxiv.org/abs/chao-dyn/9807013v1

Physica D 132 (1999) 393

Nonlinear Sciences

Chaotic Dynamics

20 pages in LaTex + 3 figures in ps, submitted to Physica D

Scientific paper

We analyze dynamical properties of a "gap-tent map" - a family of 1D maps with a symmetric gap, which mimics the presence of noise in physical realizations of chaotic systems. We demonstrate that the dependence of the topological entropy on the size of the gap has a structure of the devil's staircase. By integrating over a fractal measure, we obtain analytical, piece-wise differentiable approximations of this dependence. Applying concepts of the kneading theory we find the position and the values of the entropy for all leading entropy plateaus. Similar properties hold also for the dependence of the fractal dimension of the invariant set and the escape rate.

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